Related papers: Pointwise Green function bounds and stability of c…
Recently, Benzoni--Gavage, Danchin, Descombes, and Jamet have given a sufficient condition for linear and nonlinear stability of solitary wave solutions of Korteweg's model for phase-transitional isentropic gas dynamics in terms of…
We prove the non-linear stability of a class of travelling-wave solutions to the extended Aw-Rascle system with a singular offset function, which is formally equivalent to the compressible pressureless Navier-Stokes system with a singular…
The Navier--Stokes order hydrodynamic equations for a low-density driven granular mixture obtained previously [Khalil and Garz\'o, Phys. Rev. E \textbf{88}, 052201 (2013)] from the Chapman--Enskog solution to the Boltzmann equation are…
Extending previous work with Lattanzio and Mascia on the scalar (in fluid-dynamical variables) Hamer model for a radiative gas, we show nonlinear orbital asymptotic stability of small-amplitude shock profiles of general systems of coupled…
In this article we study the spectral, linear and nonlinear stability of stationary shock profile solutions to the Lax-Wendroff scheme for hyperbolic conservation laws. We first clarify the spectral stability of such solutions depending on…
The pointwise space-time behavior of the Green's function of the three-dimensional modified Vlasov-Poisson-Boltzmann system is studied in this paper. It is shown that the Green's function has a decomposition of the macroscopic diffusive…
We consider the problem of spectral stability of traveling wave solutions $u=\gamma(x-Wt)$ for a system of viscous conservation laws $\partial_t u + \partial_x F(u) = \partial^2_x u$. Such solutions correspond to heteroclinic trajectories…
A free boundary problem for the one-dimensional compressible Navier-Stokes equations is investigated. The asymptotic stability of the viscous shock wave is established under some smallness conditions. The proof is given by an elementary…
In this note, we show the existence of regular solutions to the stationary version of the Navier-Stokes system for compressible fluids with a density dependent viscosity, known as the shallow water equations. For arbitrary large forcing we…
We show that transition to longitudinal instability of strong detonation solutions of reactive compressible Navier--Stokes equations is generically associated with Hopf bifurcation to nearby time-periodic "galloping", or "pulsating",…
This paper is concerned with nonlinear stability of viscous contact discontinuity to a free boundary problem for the one-dimensional full compressible Navier-Stokes equations in half space $[0,\infty)$. For the case when the local stability…
We establish the global well-posedness theory of small BV weak solutions to a one-dimensional compressible Navier--Stokes model for reacting gas mixtures in dynamic combustion. The unknowns of the PDE system consist of the specific volume,…
We study by a combination of numerical and analytical Evans function techniques the stability of solitary wave solutions of the St. Venant equations for viscous shallow-water flow down an incline, and related models. Our main result is to…
We summarize recent progress on one- and multi-dimensional stability of viscous shock wave solutions of compressible Navier--Stokes equations and related symmetrizable hyperbolic--parabolic systems, with an emphasis on the large-amplitude…
We study front solutions of a system that models combustion in highly hydraulically resistant porous media. The spectral stability of the fronts is tackled by a combination of energy estimates and numerical Evans function computations. Our…
We prove that traveling waves in viscous compressible liquids are a generic phenomenon. The setting for our result is a horizontally infinite, finite depth layer of compressible, barotropic, viscous fluid, modeled by the free boundary…
We carry out a systematic analytical and numerical study of spectral stability of discontinuous roll wave solutions of the inviscid Saint Venant equations, based on a periodic Evans-Lopatinski determinant analogous to the periodic Evans…
We consider stability of non-rotating viscous gaseous stars modeled by the Navier-Stokes-Poisson system. Under general assumptions on the equations of states, we proved that the number of unstable modes for the linearized…
We prove the linear orbital stability of spectrally stable stationary discrete shock profiles for conservative finite difference schemes applied to systems of conservation laws. The proof relies on an accurate description of the pointwise…
We study Green functions for stationary Stokes systems satisfying the conormal derivative boundary condition. We establish existence, uniqueness, and various estimates for the Green function under the assumption that weak solutions of the…